Quiz 23: Model Fitting, Robust Estimation, and RANSAC

. Why does ordinary least squares (OLS) give a biased line fit when both x and y coordinates are noisy?

Total least squares (TLS) measures perpendicular distance and treats both coordinates symmetrically, which is more appropriate when both x and y carry comparable noise.

. Why does ordinary least-squares fitting break catastrophically under outliers?

Squaring a large residual makes it dominate the total cost, so the fit moves away from the correct points to reduce that one huge squared term.

. What is the core strategy RANSAC uses to fit a model in the presence of outliers?

RANSAC fits from minimal random samples and picks whichever candidate has the largest consensus set, then does a final least-squares refit on just the inliers.

. According to the RANSAC iteration-count formula, why does fitting a homography (minimal sample size 4) require many more iterations than fitting a line (minimal sample size 2) at the same outlier rate?

Since the chance of an all-inlier sample is w raised to the sample size, a larger minimal sample (4 vs. 2) makes an all-inlier draw far less likely, requiring many more trials for the same confidence.